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Notation for concatenation of indexed vectors/matrices

Is there any standard notation for concatenation of matrices/vectors where their indices are taken from a set. I have matrices $A_{ij}$ where $(i,j)\in S$. I want to denote a matrix $A$ which is the ...
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How to check the availability of particular function [on hold]

I want to check the availability of particular function that returns the value of results in binary like 0 or 1....How to check these function using mathematics...
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What's the correct notation for a minimum of a row of a matrix?

Let I=1,...,m denote the indexes of the rows of a matrix A Let J=1,...,n denote the indexes of the columns of a matrix A Let xi,j denote the value of the element A[i,j] I need do use a notation to ...
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If I want to solve a system of linear equations, like 2x-y=1 x+2y=4 Then the matrix notation for the same would be: $$\begin{bmatrix} 2 & -1 \\ 1 & 2 \\ \end{bmatrix} \begin{bmatrix} X\\ ... 2answers 94 views Matrix-Multiplication I have to matrices:$$A=\pmatrix{1&a&1\\1&0&a\\1&2&0} ; \quad B= \pmatrix{1&b&3\\2&1&0}$$The task is to determine AB, AB^T, BA I think i cannot ... 1answer 24 views Notation for matrix and sum of matrix rows I have a table that describes the influence of sources (columns) on sinks (rows) where rows=(A,B,C) and columns=(A,B,C,D,E). So my table looks like: ... 0answers 21 views element subset for adjacency matrix I am trying to create an element of a matrix that is a subset of a larger matrix. However, I am told that my subscripts do not match. I wanted other people's opinion as to what I am doing wrong and ... 1answer 23 views Basic matrice notation I want to compute the L2 distance between a set of points X and M using matrices, for that I proceed as follows: 1) I substract both matrices, X-M 2) I square each matrice member (X-M)^2 3) I ... 0answers 21 views Column or row of a matrix? The question is so simple, but I cannot find the answer. Is M_i (usually) the i^{\text{th}} column of matrix M? Or the i^{\text{th}} row? Since M_{ij} is the j^{\text{th}} element of the ... 1answer 38 views \mathbb{R}_* Notation What does the notation \mathbb{R}_* denote? I am seeing it used for showing domain of matrices, M\in \mathbb{R}_*^{a \times b}, which is different from N \in \mathbb{R}^{a \times b}. But I do ... 0answers 52 views Notation in Linear Algebra What does (A\mid b) denote in Linear Algebra? Specifically in the context of the following question: "If (A\mid b) is in reduced row echelon form, prove that A is also in reduced row echelon ... 1answer 46 views Is there a way in matrix math notation to show the 'flip up-down', and 'flip left-right' of a matrix? Title says it all - is there an accepted mathematical way in matrix notation to show those operations on a matrix? Thanks. 0answers 36 views problems on define set with polynomials I'm trying to say set A is the set of nonnegative integers that not of this two forms 3x^2 + (6y-4)x - y\  and \ 3x^2 + (6y-2)x + (y - 1), for example: 4=3 \cdot1^2+(6 \cdot1-4) \cdot 1-1\  is ... 0answers 21 views Notation for appending 2 submatrices I have a matrix M with i rows and (e+n) columns: M_{i,e+n} I would like to express that M_{i,e+n} is the result of appending M_{i,e} and M_{i,n} What is the algebraic notation to ... 0answers 8 views Question about notation matrix of partial derivatives where one component has two indices lets suppose we have a vector (\delta_{11}, \delta_{12}, \dots, \delta_{jk}) where \delta_{jk} = \alpha_j + \beta_k, i.e., each element is build up of two components. The first index j specifies ... 2answers 30 views Looking for notation of set of all entries of some matrix? I'm busy writing my thesis, and I'm looking for some concise notation to denote the supremum of the matrix entries of, say A \in M_n(\mathbb{R}). How should I do this? Looking for something like ... 2answers 47 views Notation - Transpose of Block Matrices [Lay P121 Q2.4.12] Definition of Transpose is (A^T)_{ij} = A_{ji} 1. Why \begin{bmatrix} M & N \end{bmatrix}^T = \begin{bmatrix} M^T \\ N^T \end{bmatrix}, and NOT \begin{bmatrix} M \\ N\end{bmatrix}? ... 4answers 395 views Matrix Mathematical Notation I am trying to work out the mathematical notation for combining the columns of two matrices,$$A=\begin{pmatrix}1 & 3 & 5 \\ 2 & 4 & 1 \\ 3 & 7 & 9\end{pmatrix}$$and ... 0answers 54 views What is the Δ above the = symbol? I am reading this and at equation 4.21 it has an equal symbol with a Δ above it. Do you know how this is called, and what it does? Thanks 1answer 33 views How to define a set for a matrix I have a big matrix and I have partitioned it. So, I want to say that I am taking the summation of entries that do not belong to the blocks in the diagonal. How can I say it mathematically. Is it ... 2answers 60 views What is this form of 'notation' called? I was reading some of Max Tegmark's lecture materials and I found this little thing. Is there a name for it? Specifically, I am talking about S_1 R S_2 & S_1 R S_2 and the matrix. Is ... 0answers 27 views A question regarding notation of equation I'm reading a research paper, and, have come across this summation equation$$ S_{2} = \sum_{N -1}^{j = 0}w_{j}^{2}\cdot $$My question is: if j = 0..... N-1 do I ... 2answers 152 views Notation for summing all elements under the diagonal of a square matrix I have a simple question: What is the notation for summing all elements under the diagonal of a square matrix? I appreciate your help. 0answers 70 views Notation for Kronecker product of a matrix and itself? What is the notation for the Kronecker product of a matrix and itself? In other words, is there a short-hand way I can express the following: X⊗X X⊗X⊗X X⊗X⊗X⊗X Where X is a matrix? What ... 3answers 175 views Basic question: what does the notation [A,B] mean? If A and B are both matrices, what is [A,B]? I understand that it is a commutator and that [A,B]=AB-BA, but since I don't know what a commutator is, none of this information is telling me ... 1answer 57 views Aggregating a vector of 1\times K into a vector 1\times J, such as J<K I am stuck with a matrix algebra operation: how do I do (and mainly which notation to use) to aggregate the numbers of a vector 1\times K into a vector of 1\times J, such as J is of course lower ... 1answer 115 views Notation for the set of symmetric matrices and symmetric positive definite matrices I would like to know if there exists a notation for the set of symmetric matrices and symmetric positive definite matrices. For instance, the set of N \times N matrices with real entries is denoted ... 0answers 43 views Alternate convention in matrix multiplication? I'm going through Halmos's Finite-Dimensional Vectorspaces. I noticed an oddity in a proof where the indexes seemed to be swapped when multiplying a matrix by a vector. I went back about 30 pages to ... 0answers 245 views What is the modern use of \bigodot sign? I've seen \bigodot used in various contexts. It's used for a special set theory operation by some authors (say, Saks) and as sign for Hadamard product by a couple other authors (say, Wiener) in the ... 1answer 62 views Matrix notation: Does empty space means a bunch of zeros? I don't understand what is meant with the following notation: I think this means that the first row = 4 2 0 ... 0 second row = 1 4 1 0 ... 0 third row = 0 1 4 1 0 .. 0 etc. Is this correct ? 1answer 106 views Clarification on matrix notation subscript and superscript notation If a matrix C exists in integers \mathcal{Z}_q^{mxl} what does this mean? 2answers 34 views What is the term to make one matrix from two or more? I am looking for the proper term for the operation of creating one block matrix from two or more for example [AB] from A, B. And what is the correct notation to denote such a matrix. Do we use a ... 1answer 135 views How to express this in matrix notation (row-wise normalisation) My questions are: How do I describe the row sum of a matrix? How do I describe the number of non-zero elements per row of a matrix in matrix notation? How do I divide a vector elementwise? To give ... 2answers 103 views Matrix (correct) notation Say I have a real m \times n matrix \mathbf{M}. Shall I write \mathbf{M} \in \mathbb{R}^{m \times n} or \mathbf{M} \in \mathbb{R}^{m,n}? What is commonly accepted and most beautiful and ... 2answers 620 views Bar symbol over a matrix So I am reading a paper (not online) and I come across a definition:$$\mathbb E=R\bar R$$Where R is a complex matrix. I am thinking that it means complex conjugate, but I honestly have never seen ... 1answer 283 views How to denote matrix concatenation? Trivial question: Is there any standard notation for the concatenation of two or more matrices? Example:$$A = \left(\begin{array}[c c] - a_1 & a_2\\ a_3 & a_4 \end{array}\right),B = ...
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Help, help, help! I've come across this maths symbol, $[n(i,j)]^{0.5}$ where $n$ is a square matrix. Does this mean that it is the $(i,j)$ element of $n^{0.5}$? or $n(i,j)^{0.5}$? source: ...
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What does the following symbol mean? (direct sum? o-plus? — subject: matrix theory)

In this paper equation 11, the author uses a symbol that is a cross in a circle. I believe I have seen that referred to as a direct sum, but I am not completely sure what that is. $$\bigoplus$$ ...
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What is this notation relating to the Jacobian matrix operation?

In the below image, in the very bottom-most equation is the partial differential at the end of the equation being multiplied to every element in the inverse Jacobian matrix (and then beta_n added)? Or ...
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What does this notation mean? Set of real numbers transposed??

In the below: from top of Page 13: http://www.ntuzov.com/Nik_Site/Niks_files/Research/papers/stat_arb/Ahmed_2009.pdf how do you interpret what x is an element of? It looks like the set of real ...
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Representing $m\times n$ matrix using ordered $n$-tuples and an $m$-tuple

Can a matrix, generally \begin{bmatrix} a_{1,1} &\cdots &a_{1,n} \\ \vdots &\ddots & \vdots \\ a_{m,1} &\cdots &a_{m,n} \end{bmatrix} be represented using ordered ...
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Ambiguous notation for squared matrix

What does $A^{2}$ mean for square $A$? Is it $AA$ or $AA^{T}$? Sometimes, the result may differ. Or there is no uniform approach?
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Is there a symbol for matrix multiplication operator?

Title says it all. Is there any specific operator symbol for matrix multiplication? Not just write down side by side but symbols like cross ($\times$).
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What is the notation for the set of all $m\times n$ matrices?

Given that $\mathbb{R}^n$ is the notation used for n-dimensional vectors, is there an accepted equivalent notation for matrices?
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$^t$, $^\dagger$, $^*$, $^H$, $^⊤$, and $^T$ : Which is which, and what do each mean?

I think this question's answer(s) will be of profound use to the future generation of human beings who happen to stumble upon the website math.stackexchange.com. What are the differences between ...
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Simplified matrix notation

There is a mathematical notation to define an array that you can write using standard keyboard characters on one line? for example:   1 3 8 7 10 17 22 6   5 10 23 8 11 98 7 12
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Is there a name for this given type of matrix?

Given a finite set of symbols, say $\Omega=\{1,\ldots,n\}$, is there a name for an $n\times m$ matrix $A$ such that every column of $A$ contains each elements of $\Omega$? (The motivation for this ...
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Notation minimum of a column vector

I'd like to know the notation to express the minimum of a column vector. Is this notation correct? \min \left[\matrix{ \left|b_{n}-b_{n+1}\right| \cr ...
$(\mathbf{u}^T\mathbf{v})\mathbf{v} = \mathbf{u}^T(\mathbf{v}\mathbf{v})$ doesn't hold for $\mathbf{u}, \mathbf{v}\in\mathbb{R}^n$ - why?
Suppose I have vectors $\mathbf{u}$ and $\mathbf{v}$ in $\mathbb{R}^n$. It is well defined to write $5\mathbf{v}$ or $c\mathbf{v}$ for scalar $c$. Since the inner product of $\mathbf{u}$ and ...
I'm working with a set of $M$ vectors $\{\mathbf{w}_i \in \mathbb{R}^N, \, i = 1, \ldots, M \}$. Since single vectors are usually considered as column vectors, I'm defining a matrix  \mathbf{W} = ...